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You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60

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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Bunuel wrote:
sandal85 wrote:
You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 centimeters. The number of non-congruent triangles that can be formed by choosing three of the sticks to make the sides is

A. 3
B. 6
C. 7
D. 10
E. 12

OA will be posted after some time.

Please inclease my Kudos if you like the problem...

The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Based on this there can be only 7 triangles formed: (20, 30, 40), (20, 40, 50), (20, 50, 60), (30, 40, 50), (30, 40, 60), (30, 50, 60), (40, 50, 60).

Hi Bunuel,

Is there any other method (combinatorics) to solve this question ?
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
Got this correct but spent 3.48
Used trial and error, keeping the basic properties of triangle in mind.

Anybody has a better / faster method??

Thanks.
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You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
1st, you can not form a valid triangle with any other 2 sides if 1 of the Sides picked =10. The Triangle will always fail the Triangle Test for Validity (the 2 Smaller Side Lengths will NEVER be greater than > Longest Side Length)

The 7 Triangles that will work after using the TEST: 2 Shorter Side Lengths > 3rd Longest Side Length

20 - 30 - 40

20 - 40 - 50

20 - 50 - 60

30 - 40 - 50

30 - 40 - 60

30 - 50 - 60

40 - 50 - 60

Since there are only "5 Choose 3" = 20 Different Combinations of 3 Sticks Picked, if you can quickly realize that 10 can never be a valid Side for Any Triangle formed with any of the 2 other sides given, you can cut that down to 10 Triangle Values that you need to Test.

Moving quickly, it's possible to get it finished within 2 - 3 minutes.

EDIT: I said it's "possible. I didn't say I was able to do it lol.
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
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Re: You have 6 sticks of lengths 10, 20, 30, 40, 50, and 60 [#permalink]
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